Tessellation
Definition

A tessellation occurs when a shape is repeated over and over again covering a plane without any gaps or overlaps.

The shape is "repeated" by the basic transformations of translations and/or reflections and/or rotations.


Tessellation of a regular hexagon

The regular hexagon above can form the tessellation by translations, reflections or rotations.

Not all shapes form tessellations.


Examples

The scalene triangle below forms a tessellation

Tessellation of a scalene triangle

The "arrow" shape below forms a tessellation

Tessellation of a scalene triangle

The composite figure below forms a tessellation

Tessellation of a composite figure

The regular pentagon shape below DOES NOT form a tessellation. Whenever gaps or overlaps are not preventable, a tessellation cannot be formed.

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